A polysyllogism is a string of any number of proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

s forming together a sequence of syllogism

Syllogism

A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

s such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on. Each constituent syllogism is called a prosyllogism except the very last, because the conclusion of the last syllogism is not a premise for another syllogism. For example:

It is raining.

If we go out while it is raining we will get wet.

If we get wet, we will get cold.

Therefore, if we go out we will get cold.

Examination of the structure of the argument reveals the following sequence of constituent (pro)syllogisms:

It is raining.

If we go out while it is raining we will get wet.

Therefore, if we go out we will get wet.

If we go out we will get wet.

If we get wet, we will get cold.

Therefore, if we go out we will get cold.

A sorites is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise. Example:

All lions are big cats.

All big cats are predators.

All predators are carnivores.

Therefore, all lions are carnivores.

The word "sorites" (icon) comes from "the fallacy of the heap

Sorites paradox

The sorites paradox is a paradox that arises from vague predicates. The paradox of the heap is an example of this paradox which arises when one considers a heap of sand, from which grains are individually removed...

", from σωρός "heap" or "pile". In other words, a sorites is a heap of propositions chained together.

Lewis Carroll

Lewis Carroll

Charles Lutwidge Dodgson , better known by the pseudonym Lewis Carroll , was an English author, mathematician, logician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the...

uses sorites in his book Symbolic Logic. Here is an example http://durendal.org/lcsl/SymbolicLogic.txt:

No experienced person is incompetent;

Jenkins is always blundering;

No competent person is always blundering.

Jenkins is inexperienced.

Carroll's example may be translated thus

All experienced persons are competent persons.

No competent persons are blunderers.

Jenkins is a blunderer.

Jenkins is not an experienced person.